Method and apparatus for multiple input multiple output (MIMO) transmit beamforming

ABSTRACT

A wireless communications network is provided. The wireless communications network comprises a plurality of base stations. Each one of said base stations is capable of wireless communications with a plurality of subscriber stations. At least one of said plurality of base stations comprises a processor configured to select a codeword from a codebook and precode data with the selected codeword, and a transmitter configured to transmit the precoded data. Rank 1 of the codebook is selected from the following algorithm: 
     
       
         
               
               
               
               
             
                   
                   
               
                   
                 Codebook Matrix Index 
                   
                   
               
                   
                 (CMI) 
                 Base Matrix 
                 Rank 1 
               
                   
                   
               
                   
               
               
               
               
               
             
                   
                 1 
                 V8(:,:,3) 
                 V8(:,1,3) 
               
                   
                 2 
                   
                 V8(:,2,3) 
               
                   
                 3 
                   
                 V8(:,3,3) 
               
                   
                 4 
                   
                 V8(:,4,3) 
               
                   
                 5 
                   
                 V8(:,5,3) 
               
                   
                 6 
                   
                 V8(:,6,3) 
               
                   
                 7 
                   
                 V8(:,7,3) 
               
                   
                 8 
                   
                 V8(:,8,3) 
               
                   
                 9 
                   
                 V8(:,9,3) 
               
                   
                 10 
                   
                 V8(:,10,3) 
               
                   
                 11 
                   
                 V8(:,11,3) 
               
                   
                 12 
                   
                 V8(:,12,3) 
               
                   
                 13 
                   
                 V8(:,13,3) 
               
                   
                 14 
                   
                 V8(:,14,3) 
               
                   
                 15 
                   
                 V8(:,15,3) 
               
                   
                 16 
                   
                 V8(:,16,3)

CROSS-REFERENCE TO RELATED APPLICATION(S) AND CLAIM OF PRIORITY

The present application is related to U.S. Provisional Patent No.61/208,518, filed Feb. 25, 2009, entitled “METHOD AND APPARATUS FORMULTI-USER CLOSED-LOOP TRANSMIT BEAMFORMING (MU-CLTB) WITH 8 TRANSMITANTENNA IN OFDM WIRELESS SYSTEMS”. Provisional Patent No. 61/208,518 isassigned to the assignee of the present application and is herebyincorporated by reference into the present application as if fully setforth herein. The present application hereby claims priority under 35U.S.C. §119(e) to U.S. Provisional Patent No. 61/208,518.

The present application also is related to U.S. Provisional Patent No.61/209,145, filed Mar. 4, 2009, entitled “METHOD AND APPARATUS FORMULTI-USER CLOSED-LOOP TRANSMIT BEAMFORMING (MU-CLTB) WITH 8 TRANSMITANTENNA IN OFDM WIRELESS SYSTEMS”. Provisional Patent No. 61/209,145 isassigned to the assignee of the present application and is herebyincorporated by reference into the present application as if fully setforth herein. The present application hereby claims priority under 35U.S.C. §119(e) to U.S. Provisional Patent No. 61/209,145.

TECHNICAL FIELD OF THE INVENTION

The present application relates generally to wireless communicationsystems and, more specifically, to beamforming in wireless communicationsystems.

BACKGROUND OF THE INVENTION

Transmit beamforming in wireless systems can be performed in either aclosed-loop or an open-loop manner. An open-loop system is well suitedfor Time Division Duplexing (TDD) systems. An open-loop system does notrequire channel information feedback. As a result, less overhead isrequired. However, the disadvantage of an open-loop system is that thesystem needs to constantly conduct phase calibration in order tocompensate for the phase difference between the transmission andreception Radio Frequency (RF) chains among the multiple transmitantennas. Another disadvantage of an open-loop system is that the systemrequires a constant uplink phase reference such as uplink pilots. Thisrequirement could lead to an excessive feedback overhead. The process ofphase calibration is generally costly and sensitive to radio channelenvironment.

A closed-loop system, on the other hand, does not require phasecalibration process. However, a closed-loop system does require channelfeedback to the transmitter, which results in additional overhead.Furthermore, a closed-loop system is also sensitive to feedback channelerror due to feedback delay or fast channel variation. Typically,Frequency Division Duplexing (FDD) systems employ closed-loop transmitbeamforming schemes. However, a closed-loop scheme also can be appliedto TDD systems.

SUMMARY OF THE INVENTION

A wireless communications network is provided. The wirelesscommunications network comprises a plurality of base stations. Each oneof said base stations is capable of wireless communications with aplurality of subscriber stations. At least one of said plurality of basestations comprises a processor configured to select a codeword from acodebook and precode data with the selected codeword, and a transmitterconfigured to transmit the precoded data. Rank 1 of the codebook isselected from the following algorithm:

Codebook Matrix Index (CMI) Base Matrix Rank 1 1 V8(:,:,3) V8(:,1,3) 2V8(:,2,3) 3 V8(:,3,3) 4 V8(:,4,3) 5 V8(:,5,3) 6 V8(:,6,3) 7 V8(:,7,3) 8V8(:,8,3) 9 V8(:,9,3) 10 V8(:,10,3) 11 V8(:,11,3) 12 V8(:,12,3) 13V8(:,13,3) 14 V8(:,14,3) 15 V8(:,15,3) 16 V8(:,16,3)

A wireless communications network is provided. The wirelesscommunications network comprises a plurality of base stations. Each oneof said base stations is capable of wireless communications with aplurality of subscriber stations. At least one of said plurality of basestations comprises a processor configured to select a codeword from acodebook and precode data with the selected codeword, and a transmitterconfigured to transmit the precoded data. Ranks 3 to 8 of the codebookare selected from the following algorithms:

Codebook Matrix Base Index (CMI) Matrix Rank3 Rank4 Rank5 Rank6 Rank7Rank8 1 V8(:, :, 1) 135 1537 12357 123567 1234567 12345678 2 246 264812468 124568 1234568 n/a 3 237 3726 23467 234678 1234678 n/a 4 148 481513458 134578 1234578 n/a 5 357 5372 23567 234567 2345678 n/a 6 468 648114568 134568 1345678 n/a 7 267 7264 24678 124678 1245678 n/a 8 158 815313578 123578 1235678 n/a 9 V8(:, :, 2) 123 1234 12345 123456 123456712345678 10 124 1246 12456 124567 1245678 n/a 11 234 2437 23478 1234781234578 n/a 12 134 1348 13478 134678 1234678 n/a 13 578 3578 23578235678 1235678 n/a 14 678 4678 14678 145678 1345678 n/a 15 576 567835678 345678 2345678 n/a 16 568 1568 13568 123568 1234568 n/awhere the numbers shown in the column for each rank refer to the columnindex of the matrices V8(:,:,1) and V8(:,:,2).

A wireless communications network is provided. The wirelesscommunications network comprises a plurality of base stations. Each oneof said base stations is capable of wireless communications with aplurality of subscriber stations. At least one of said plurality of basestations comprises a processor configured to select a codeword from acodebook and precode data with the selected codeword, and a transmitterconfigured to transmit the precoded data. Ranks 1 to 8 of the codebookare selected from the following algorithm:

CW Base Matrix Index Rank1 Rank2 Rank3 Rank4 Rank5 Rank6 Rank7 Rank8$W_{1} = {\frac{1}{\sqrt{8}}{H_{1,1,1}\left( {1,1,1,1} \right)}}$  1 2  3  4  5  6  7  8 1 2 3 4 5 6 7 8 15 24 13 48 57 26 37 68 135 124 123148 567 246 237 568 1357 1247 1234 1458 5678 2468 2367 3568 12357 1247812345 14568 15678 24678 23467 34568 123567 124578 123457 124568 135678124678 234678 134568 1234567 1245678 1234578 1234568 1235678 12346782345678 1345678 12345678 n/a n/a n/a n/a n/a n/a n/a$W_{2} = {\frac{1}{\sqrt{8}}{H_{3,3,3}\left( {3,3,3,3} \right)}}$  910 11 12 13 14 15 16 1 2 3 4 5 6 7 8 13 24 35 46 57 68 17 28 135 246 357468 157 268 137 248 1357 2468 3457 4678 1257 2678 1237 2348 12357 2346834567 14678 12567 23678 12378 23458 123567 234678 134567 124678 124567123678 123578 234568 1234567 2345678 1345678 1234678 1245678 12356781234578 1234568 12345678 n/a n/a n/a n/a n/a n/a n/awhere the numbers shown in the column for each rank refer to the columnindex of the matrices

$W_{1} = {{\frac{1}{\sqrt{8}}{H_{1,1,1}\left( {1,1,1,1} \right)}\mspace{14mu} {and}\mspace{14mu} W_{2}} = {\frac{1}{\sqrt{8}}{{H_{3,3,3}\left( {3,3,3,3} \right)} \cdot}}}$

A base station is provided. The base station comprises a processorconfigured to select a codeword from a codebook and precode data withthe selected codeword, and a transmitter configured to transmit theprecoded data. Rank 1 of the codebook is selected from the followingalgorithm:

Codebook Matrix Index (CMI) Base Matrix Rank 1 1 V8(:,:,3) V8(:,1,3) 2V8(:,2,3) 3 V8(:,3,3) 4 V8(:,4,3) 5 V8(:,5,3) 6 V8(:,6,3) 7 V8(:,7,3) 8V8(:,8,3) 9 V8(:,9,3) 10 V8(:,10,3) 11 V8(:,11,3) 12 V8(:,12,3) 13V8(:,13,3) 14 V8(:,14,3) 15 V8(:,15,3) 16 V8(:,16,3)

A base station is provided. The base station comprises a processorconfigured to select a codeword from a codebook and precode data withthe selected codeword, and a transmitter configured to transmit theprecoded data. Ranks 3 to 8 of the codebook are selected from thefollowing algorithms:

Codebook Matrix Base Index (CMI) Matrix Rank3 Rank4 Rank5 Rank6 Rank7Rank8 1 V8(:, :, 1) 135 1537 12357 123567 1234567 12345678 2 246 264812468 124568 1234568 n/a 3 237 3726 23467 234678 1234678 n/a 4 148 481513458 134578 1234578 n/a 5 357 5372 23567 234567 2345678 n/a 6 468 648114568 134568 1345678 n/a 7 267 7264 24678 124678 1245678 n/a 8 158 815313578 123578 1235678 n/a 9 V8(:, :, 2) 123 1234 12345 123456 123456712345678 10 124 1246 12456 124567 1245678 n/a 11 234 2437 23478 1234781234578 n/a 12 134 1348 13478 134678 1234678 n/a 13 578 3578 23578235678 1235678 n/a 14 678 4678 14678 145678 1345678 n/a 15 576 567835678 345678 2345678 n/a 16 568 1568 13568 123568 1234568 n/awhere the numbers shown in the column for each rank refer to the columnindex of the matrices V8(:,:,1) and V8(:,:,2).

A base station is provided. The base station comprises a processorconfigured to select a codeword from a codebook and precode data withthe selected codeword, and a transmitter configured to transmit theprecoded data. Ranks 1 to 8 of the codebook are selected from thefollowing algorithm:

CW Base Matrix Index Rank1 Rank2 Rank3 Rank4 Rank5 Rank6 Rank7 Rank8$W_{1} = {\frac{1}{\sqrt{8}}{H_{1,1,1}\left( {1,1,1,1} \right)}}$  1 2  3  4  5  6  7  8 1 2 3 4 5 6 7 8 15 24 13 48 57 26 37 68 135 124 123148 567 246 237 568 1357 1247 1234 1458 5678 2468 2367 3568 12357 1247812345 14568 15678 24678 23467 34568 123567 124578 123457 124568 135678124678 234678 134568 1234567 1245678 1234578 1234568 1235678 12346782345678 1345678 12345678 n/a n/a n/a n/a n/a n/a n/a$W_{2} = {\frac{1}{\sqrt{8}}{H_{3,3,3}\left( {3,3,3,3} \right)}}$  910 11 12 13 14 15 16 1 2 3 4 5 6 7 8 13 24 35 46 57 68 17 28 135 246 357468 157 268 137 248 1357 2468 3457 4678 1257 2678 1237 2348 12357 2346834567 14678 12567 23678 12378 23458 123567 234678 134567 124678 124567123678 123578 234568 1234567 2345678 1345678 1234678 1245678 12356781234578 1234568 12345678 n/a n/a n/a n/a n/a n/a n/awhere the numbers shown in the column for each rank refer to the columnindex of the matrices

$W_{1} = {{\frac{1}{\sqrt{8}}{H_{1,1,1}\left( {1,1,1,1} \right)}\mspace{14mu} {and}\mspace{14mu} W_{2}} = {\frac{1}{\sqrt{8}}{{H_{3,3,3}\left( {3,3,3,3} \right)}.}}}$

A method of operating a base station is provided. The method comprisesselecting a codeword from a codebook, precoding data with the selectedcodeword; and transmitting the precoded data. Rank 1 of the codebook isselected from the following algorithm:

Codebook Matrix Index (CMI) Base Matrix Rank 1 1 V8(:,:,3) V8(:,1,3) 2V8(:,2,3) 3 V8(:,3,3) 4 V8(:,4,3) 5 V8(:,5,3) 6 V8(:,6,3) 7 V8(:,7,3) 8V8(:,8,3) 9 V8(:,9,3) 10 V8(:,10,3) 11 V8(:,11,3) 12 V8(:,12,3) 13V8(:,13,3) 14 V8(:,14,3) 15 V8(:,15,3) 16 V8(:,16,3)

A method of operating a base station is provided. The method comprisesselecting a codeword from a codebook, precoding data with the selectedcodeword; and transmitting the precoded data. Ranks 3 to 8 of thecodebook are selected from the following algorithms:

Codebook Matrix Base Index (CMI) Matrix Rank3 Rank4 Rank5 Rank6 Rank7Rank8 1 V8(:, :, 1) 135 1537 12357 123567 1234567 12345678 2 246 264812468 124568 1234568 n/a 3 237 3726 23467 234678 1234678 n/a 4 148 481513458 134578 1234578 n/a 5 357 5372 23567 234567 2345678 n/a 6 468 648114568 134568 1345678 n/a 7 267 7264 24678 124678 1245678 n/a 8 158 815313578 123578 1235678 n/a 9 V8(:, :, 2) 123 1234 12345 123456 123456712345678 10 124 1246 12456 124567 1245678 n/a 11 234 2437 23478 1234781234578 n/a 12 134 1348 13478 134678 1234678 n/a 13 578 3578 23578235678 1235678 n/a 14 678 4678 14678 145678 1345678 n/a 15 576 567835678 345678 2345678 n/a 16 568 1568 13568 123568 1234568 n/awhere the numbers shown in the column for each rank refer to the columnindex of the matrices V8(:,:,1) and V8(:,:,2).

A method of operating a base station is provided. The method comprisesselecting a codeword from a codebook, precoding data with the selectedcodeword; and transmitting the precoded data. Ranks 1 to 8 of thecodebook are selected from the following algorithm:

CW Base Matrix Index Rank1 Rank2 Rank3 Rank4 Rank5 Rank6 Rank7 Rank8$W_{1} = {\frac{1}{\sqrt{8}}{H_{1,1,1}\left( {1,1,1,1} \right)}}$  1 2  3  4  5  6  7  8 1 2 3 4 5 6 7 8 15 24 13 48 57 26 37 68 135 124 123148 567 246 237 568 1357 1247 1234 1458 5678 2468 2367 3568 12357 1247812345 14568 15678 24678 23467 34568 123567 124578 123457 124568 135678124678 234678 134568 1234567 1245678 1234578 1234568 1235678 12346782345678 1345678 12345678 n/a n/a n/a n/a n/a n/a n/a$W_{2} = {\frac{1}{\sqrt{8}}{H_{3,3,3}\left( {3,3,3,3} \right)}}$  910 11 12 13 14 15 16 1 2 3 4 5 6 7 8 13 24 35 46 57 68 17 28 135 246 357468 157 268 137 248 1357 2468 3457 4678 1257 2678 1237 2348 12357 2346834567 14678 12567 23678 12378 23458 123567 234678 134567 124678 124567123678 123578 234568 1234567 2345678 1345678 1234678 1245678 12356781234578 1234568 12345678 n/a n/a n/a n/a n/a n/a n/awhere the numbers shown in the column for each rank refer to the columnindex of the matrices

$W_{1} = {{\frac{1}{\sqrt{8}}{H_{1,1,1}\left( {1,1,1,1} \right)}\mspace{14mu} {and}\mspace{14mu} W_{2}} = {\frac{1}{\sqrt{8}}{{H_{3,3,3}\left( {3,3,3,3} \right)}.}}}$

Before undertaking the DETAILED DESCRIPTION OF THE INVENTION below, itmay be advantageous to set forth definitions of certain words andphrases used throughout this patent document: the terms “include” and“comprise,” as well as derivatives thereof, mean inclusion withoutlimitation; the term “or,” is inclusive, meaning and/or; the phrases“associated with” and “associated therewith,” as well as derivativesthereof, may mean to include, be included within, interconnect with,contain, be contained within, connect to or with, couple to or with, becommunicable with, cooperate with, interleave, juxtapose, be proximateto, be bound to or with, have, have a property of, or the like; and theterm “controller” means any device, system or part thereof that controlsat least one operation, such a device may be implemented in hardware,firmware or software, or some combination of at least two of the same.It should be noted that the functionality associated with any particularcontroller may be centralized or distributed, whether locally orremotely. Definitions for certain words and phrases are providedthroughout this patent document, those of ordinary skill in the artshould understand that in many, if not most instances, such definitionsapply to prior, as well as future uses of such defined words andphrases.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present disclosure and itsadvantages, reference is now made to the following description taken inconjunction with the accompanying drawings, in which like referencenumerals represent like parts:

FIG. 1 illustrates an exemplary wireless network that transmits messagesin the uplink according to the principles of this disclosure;

FIG. 2 illustrates an exemplary base station in greater detail accordingto one embodiment of this disclosure;

FIG. 3 illustrates an exemplary wireless subscriber station in greaterdetail according to one embodiment of this disclosure;

FIG. 4 illustrates a diagram of a base station in communication with aplurality of mobile stations according to an embodiment of thisdisclosure;

FIG. 5 illustrates a 4×4 MIMO system according to an embodiment of thisdisclosure;

FIG. 6 illustrates a Spatial Division Multiple Access (SDMA) schemeaccording to an embodiment of this disclosure;

FIG. 7 illustrates a one-stage complex Hadamard (CH) transformationaccording to an embodiment of this disclosure;

FIG. 8 illustrates a two-stage CH transformation according to anembodiment of this disclosure;

FIG. 9 illustrates an N-stage CH transformation according to anembodiment of this disclosure;

FIG. 10A illustrates a codebook that shows a mapping from a base matrixto a codeword according to an embodiment of this disclosure;

FIG. 10B illustrates a table further describing rank 1 of the codebookof FIG. 10A according to an embodiment of this disclosure;

FIG. 11 illustrates two rank-8 matrices and according to an embodimentof this disclosure;

FIG. 12 illustrates a codebook that shows a mapping from a base matrixto a codeword according to another embodiment of this disclosure;

FIG. 13 illustrates a codebook that shows a mapping from a base matrixto a codeword according to yet another embodiment of this disclosure;

FIG. 14 illustrates a codebook that shows a mapping from a base matrixto a codeword according to a further embodiment of this disclosure;

FIG. 15 illustrates a codebook that shows a mapping from a base matrixto a codeword according to yet a further embodiment of this disclosure;

FIG. 16 is a diagram illustrating a system's performance utilizing thecodebook of FIGS. 10A and 10B according to an embodiment of thisdisclosure.

FIG. 17 illustrates a method of operating a base station according to anembodiment of this disclosure; and

FIG. 18 illustrates a method of operating a mobile or subscriber stationaccording to an embodiment of this disclosure.

DETAILED DESCRIPTION OF THE INVENTION

FIGS. 1 through 18, discussed below, and the various embodiments used todescribe the principles of the present disclosure in this patentdocument are by way of illustration only and should not be construed inany way to limit the scope of the disclosure. Those skilled in the artwill understand that the principles of the present disclosure may beimplemented in any suitably arranged communication system.

FIG. 1 illustrates exemplary wireless network 100, which transmitsmessages according to the principles of this disclosure. In theillustrated embodiment, wireless network 100 includes base station (BS)101, base station (BS) 102, base station (BS) 103, and other similarbase stations (not shown).

Base station 101 is in communication with Internet 130 or a similarIP-based network (not shown).

Base station 102 provides wireless broadband access to Internet 130 to afirst plurality of subscriber stations within coverage area 120 of basestation 102. The first plurality of subscriber stations includessubscriber station 111, which may be located in a small business (SB),subscriber station 112, which may be located in an enterprise (E),subscriber station 113, which may be located in a WiFi hotspot (HS),subscriber station 114, which may be located in a first residence (R),subscriber station 115, which may be located in a second residence (R),and subscriber station 116, which may be a mobile device (M), such as acell phone, a wireless laptop, a wireless PDA, or the like.

Base station 103 provides wireless broadband access to Internet 130 to asecond plurality of subscriber stations within coverage area 125 of basestation 103. The second plurality of subscriber stations includessubscriber station 115 and subscriber station 116. In an exemplaryembodiment, base stations 101-103 may communicate with each other andwith subscriber stations 111-116 using OFDM or OFDMA techniques.

While only six subscriber stations are depicted in FIG. 1, it isunderstood that wireless network 100 may provide wireless broadbandaccess to additional subscriber stations. It is noted that subscriberstation 115 and subscriber station 116 are located on the edges of bothcoverage area 120 and coverage area 125. Subscriber station 115 andsubscriber station 116 each communicate with both base station 102 andbase station 103 and may be said to be operating in handoff mode, asknown to those of skill in the art.

Subscriber stations 111-116 may access voice, data, video, videoconferencing, and/or other broadband services via Internet 130. In anexemplary embodiment, one or more of subscriber stations 111-116 may beassociated with an access point (AP) of a WiFi WLAN. Subscriber station116 may be any of a number of mobile devices, including awireless-enabled laptop computer, personal data assistant, notebook,handheld device, or other wireless-enabled device. Subscriber stations114 and 115 may be, for example, a wireless-enabled personal computer(PC), a laptop computer, a gateway, or another device.

FIG. 2 illustrates an exemplary base station in greater detail accordingto one embodiment of this disclosure. The embodiment of base station(BS) 102 illustrated in FIG. 2 is for illustration only. Otherembodiments of the BS 102 could be used without departing from the scopeof this disclosure.

BS 102 comprises a base station controller (BSC) 210 and a basetransceiver subsystem (BTS) 220. A base station controller is a devicethat manages wireless communications resources, including basetransceiver subsystems, for specified cells within a wirelesscommunications network. A base transceiver subsystem comprises the RFtransceivers, antennas, and other electrical equipment located in eachcell site. This equipment may include air conditioning units, heatingunits, electrical supplies, telephone line interfaces, RF transmittersand RF receivers. For the purpose of simplicity and clarity inexplaining the operation of this disclosure, the base transceiversubsystem and the base station controller associated with each basetransceiver subsystem are collectively represented by BS 101, BS 102 andBS 103, respectively.

BSC 210 manages the resources in a cell site including BTS 220. BTS 220comprises a BTS controller 225, a channel controller 235, a transceiverinterface (IF) 245, an RF transceiver unit 250, and an antenna array255. Channel controller 235 comprises a plurality of channel elementsincluding an exemplary channel element 240. BTS 220 also comprises ahandoff controller 260 and a memory 270. The embodiment of handoffcontroller 260 and memory 270 included within BTS 220 is forillustration only. Handoff controller 260 and memory 270 can be locatedin other portions of BS 102 without departing from the scope of thisdisclosure.

BTS controller 225 comprises processing circuitry and memory capable ofexecuting an operating program that communicates with BSC 210 andcontrols the overall operation of BTS 220. Under normal conditions, BTScontroller 225 directs the operation of channel controller 235, whichcontains a number of channel elements including channel element 240 thatperform bi-directional communications in the forward channels and thereverse channels. A forward channel refers to a channel in which signalsare transmitted from the base station to the mobile station (alsoreferred to as DOWNLINK communications). A reverse channel refers to achannel in which signals are transmitted from the mobile station to thebase station (also referred to as UPLINK communications). In anembodiment of this disclosure, the channel elements communicateaccording to an OFDMA protocol with the mobile stations in cell 120.Transceiver IF 245 transfers the bi-directional channel signals betweenchannel controller 240 and RF transceiver unit 250. The embodiment of RFtransceiver unit 250 as a single device is for illustration only. RFtransceiver unit 250 can comprise separate transmitter and receiverdevices without departing from the scope of this disclosure.

Antenna array 255 transmits forward channel signals received from RFtransceiver unit 250 to mobile stations in the coverage area of BS 102.Antenna array 255 also sends to transceiver 250 reverse channel signalsreceived from mobile stations in the coverage area of BS 102. In someembodiments of this disclosure, antenna array 255 is a multi-sectorantenna, such as a three-sector antenna in which each antenna sector isresponsible for transmitting and receiving in a 120° arc of coveragearea. Additionally, RF transceiver 250 may contain an antenna selectionunit to select among different antennas in antenna array 255 duringtransmit and receive operations.

According to some embodiments of this disclosure, BTS controller 225 isconfigured to store a codebook 271 in memory 270. The codebook 271 isused by BS 102 to perform beamforming with a mobile station. Memory 270can be any computer readable medium. For example, the memory 270 can beany electronic, magnetic, electromagnetic, optical, electro-optical,electro-mechanical, and/or other physical device that can contain,store, communicate, propagate, or transmit a computer program, software,firmware, or data for use by the microprocessor or othercomputer-related system or method. A part of memory 270 comprises arandom access memory (RAM), and another part of memory 270 comprises aFlash memory that acts as a read-only memory (ROM).

BSC 210 is configured to maintain communications with BS 101, BS 102 andBS 103. BS 102 communicates with BS 101 and BS 103 via a wirelessconnection. In some embodiments, the wireless connection is a wire-lineconnection.

FIG. 3 illustrates an exemplary wireless subscriber station in greaterdetail according to one embodiment of this disclosure. The embodiment ofwireless subscriber station (SS) 116 illustrated in FIG. 3 is forillustration only. Other embodiments of the wireless SS 116 could beused without departing from the scope of this disclosure.

Wireless SS 116 comprises an antenna 305, a radio frequency (RF)transceiver 310, a transmit (TX) processing circuitry 315, a microphone320, and a receive (RX) processing circuitry 325. SS 116 also comprisesa speaker 330, a main processor 340, an input/output (I/O) interface(IF) 345, a keypad 350, a display 355, and a memory 360. Memory 360further comprises a basic operating system (OS) program 361 and acodebook 362 used by SS 116 to perform beamforming with a base station.

Radio frequency (RF) transceiver 310 receives from antenna 305 anincoming RF signal transmitted by a base station of wireless network100. Radio frequency (RF) transceiver 310 down-converts the incoming RFsignal to produce an intermediate frequency (IF) or a baseband signal.The IF or baseband signal is sent to receiver (RX) processing circuitry325 that produces a processed baseband signal by filtering, decoding,and/or digitizing the baseband or IF signal. Receiver (RX) processingcircuitry 325 transmits the processed baseband signal to speaker 330(i.e., voice data) or main processor 340 for further processing (e.g.,web browsing).

Transmitter (TX) processing circuitry 315 receives analog or digitalvoice data from microphone 320 or other outgoing baseband data (e.g.,web data, e-mail, interactive video game data) from main processor 340.Transmitter (TX) processing circuitry 315 encodes, multiplexes, and/ordigitizes the outgoing baseband data to produce a processed baseband orIF signal. Radio frequency (RF) transceiver 310 receives the outgoingprocessed baseband or IF signal from transmitter (TX) processingcircuitry 315. Radio frequency (RF) transceiver 310 up-converts thebaseband or IF signal to a radio frequency (RF) signal that istransmitted via antenna 305.

In some embodiments of this disclosure, main processor 340 is amicroprocessor or microcontroller. Memory 360 is coupled to mainprocessor 340. According to some embodiments of this disclosure, a partof memory 360 comprises a random access memory (RAM) and another part ofmemory 360 comprises a Flash memory that acts as a read-only memory(ROM).

Main processor 340 executes a basic operating system (OS) program 361stored in memory 360 in order to control the overall operation ofwireless SS 116. In one such operation, main processor 340 controls thereception of forward channel signals and the transmission of reversechannel signals by radio frequency (RF) transceiver 310, receiver (RX)processing circuitry 325, and transmitter (TX) processing circuitry 315in accordance with well-known principles.

Main processor 340 is capable of executing other processes and programsresident in memory 360. Main processor 340 can move data into or out ofmemory 360 as required by an executing process. Main processor 340 alsois coupled to I/O interface 345. I/O interface 345 provides SS 116 withthe ability to connect to other devices such as laptop computers andhandheld computers. I/O interface 345 is the communication path betweenthese accessories and main controller 340.

Main processor 340 also is coupled to keypad 350 and display unit 355.The operator of SS 116 uses keypad 350 to enter data into SS 116.Display 355 may be a liquid crystal display (LCD) capable of renderingtext and/or at least limited graphics from web sites. Alternateembodiments may use other types of displays.

The example of system level description for the new invention is shownin 1, where a base station is simultaneously communicated with multipleof mobile stations through the use of multiple antenna beams, eachforming an antenna beam toward its intended mobile station at the sametime and same frequency. It is noted that, in a wireless communication,the communication from a base station to a mobile station is also knownas downlink communication. The base station and mobile stations areemploying multiple antennas for transmission and reception of radio wavesignals. The radio wave signals can be Orthogonal Frequency DivisionMultiplexing (OFDM) signals. The mobile stations can be a PDA, laptop,or handheld device.

FIG. 4 illustrates a diagram 400 of a base station 420 in communicationwith a plurality of mobile stations 402, 404, 406, and 408 according toan embodiment of this disclosure.

In this embodiment, base station 420 performs simultaneous beamformingthrough a plurality of transmitters to each mobile station. Forinstance, base station 420 transmits data to mobile station 402 througha beamformed signal 410, data to mobile station 404 through a beamformedsignal 412, data to mobile station 406 through a beamformed signal 414,and data to mobile station 408 through a beamformed signal 416. In someembodiments of the present disclosure, base station 420 is capable ofsimultaneously beamforming to the mobile stations 402, 404, 406, and408. In some embodiments, each beamformed signal is formed toward itsintended mobile station at the same time and the same frequency. For thepurpose of clarity, the communication from a base station to a mobilestation may also be referred to known as downlink communication and thecommunication from a mobile station to a base station may be referred toas uplink communication.

Base station 420 and mobile stations 402, 404, 406, and 408 employmultiple antennas for transmitting and receiving wireless signals. It isunderstood that the wireless signals may be radio wave signals, and thewireless signals may use any transmission scheme known to one skilled inthe art, including an Orthogonal Frequency Division Multiplexing (OFDM)transmission scheme.

Mobile stations 402, 404, 406, and 408 may be any device that is capablereceiving wireless signals. Examples of mobile stations 402, 404, 406,and 408 include, but are not limited to, a personal data assistant(PDA), laptop, mobile telephone, handheld device, or any other devicethat is capable of receiving the beamformed transmissions.

The OFDM transmission scheme is used to multiplex data in the frequencydomain. Modulation symbols are carried on frequency sub-carriers. Thequadrature amplitude modulation (QAM) modulated symbols areserial-to-parallel converted and input to the inverse fast Fouriertransform (IFFT). At the output of the IFFT, N time-domain samples areobtained. Here N refers to the IFFT/fast Fourier transform (FFT) sizeused by the OFDM system. The signal after IFFT is parallel-to-serialconverted and a cyclic prefix (CP) is added to the signal sequence. CPis added to each OFDM symbol to avoid or mitigate the impact due tomultipath fading. The resulting sequence of samples is referred to as anOFDM symbol with a CP. At the receiver side, assuming that perfect timeand frequency synchronization are achieved, the receiver first removesthe CP, and the signal is serial-to-parallel converted before being fedinto the FFT. The output of the FFT is parallel-to-serial converted, andthe resulting QAM modulation symbols are input to the QAM demodulator.

The total bandwidth in an OFDM system is divided into narrowbandfrequency units called subcarriers. The number of subcarriers is equalto the FFT/IFFT size N used in the system. In general, the number ofsubcarriers used for data is less than N because some subcarriers at theedge of the frequency spectrum are reserved as guard subcarriers. Ingeneral, no information is transmitted on guard subcarriers.

Because each OFDM symbol has finite duration in time domain, thesub-carriers overlap with each other in frequency domain. However, theorthogonality is maintained at the sampling frequency assuming thetransmitter and receiver have perfect frequency synchronization. In thecase of frequency offset due to imperfect frequency synchronization orhigh mobility, the orthogonality of the sub-carriers at samplingfrequencies is destroyed, resulting in inter-carrier-interference (ICI).

The use of multiple transmit antennas and multiple receive antennas atboth a base station and a single mobile station to improve the capacityand reliability of a wireless communication channel is known as a SingleUser Multiple Input Multiple Output (SU-MIMO) system. A MIMO systempromises linear increase in capacity with K where K is the minimum ofnumber of transmit (M) and receive antennas (N) (i.e., K=min(M,N)). AMIMO system can be implemented with the schemes of spatial multiplexing,a transmit/receive beamforming, or transmit/receive diversity.

FIG. 5 illustrates a 4×4 MIMO system 500 according to an embodiment ofthis disclosure.

In this example, four different data streams 502 are transmittedseparately using four transmit antennas 504. The transmitted signals arereceived at four receive antennas 506 and interpreted as receivedsignals 508. Some form of spatial signal processing 510 is performed onthe received signals 508 in order to recover four data streams 512.

An example of spatial signal processing is Vertical-Bell LaboratoriesLayered Space-Time (V-BLAST), which uses the successive interferencecancellation principle to recover the transmitted data streams. Othervariants of MIMO schemes include schemes that perform some kind ofspace-time coding across the transmit antennas (e.g., Diagonal BellLaboratories Layered Space-Time (D-BLAST)). In addition, MIMO can beimplemented with a transmit/receive diversity scheme and atransmit/receive beamforming scheme to improve the link reliability orsystem capacity in wireless communication systems.

The MIMO channel estimation consists of estimating the channel gain andphase information for links from each of the transmit antennas to eachof the receive antennas. Therefore, the channel response “H” for N×MMIMO system consists of an N×M matrix, as shown in Equation 1 below:

$\begin{matrix}{H = {\begin{bmatrix}a_{11} & a_{12} & \ldots & a_{1M} \\a_{21} & a_{22} & \ldots & a_{2M} \\\vdots & \vdots & \ldots & \vdots \\a_{N\; 1} & a_{M\; 2} & \ldots & a_{NM}\end{bmatrix}.}} & \left\lbrack {{Eqn}.\mspace{14mu} 1} \right\rbrack\end{matrix}$

In Equation 1, the MIMO channel response is represented by H and a_(nm)represents the channel gain from transmit antenna n to receive antennam. In order to enable the estimations of the elements of the MIMOchannel matrix, separate pilots may be transmitted from each of thetransmit antennas.

As an extension of SU-MIMO, multi-user MIMO (MU-MIMO) is a communicationscenario where a base station with multiple transmit antennas cansimultaneously communicate with multiple mobile stations through the useof multi-user beamforming schemes such as Spatial Division MultipleAccess (SDMA) to improve the capacity and reliability of a wirelesscommunication channel.

FIG. 6 illustrates an SDMA scheme according to an embodiment of thisdisclosure.

As shown in FIG. 6, base station 320 is equipped with 8 transmitantennas while four mobile stations 302, 304, 306, and 308 are eachequipped two antennas. In this example, base station 320 has eighttransmit antennas. Each of the transmit antennas transmits one ofbeamformed signals 310, 602, 604, 312, 314, 606, 316, and 608. In thisexample, mobile station 302 receives beamformed transmissions 310 and602, mobile station 304 receives beamformed transmissions 604 and 312,mobile station 306 receives beamformed transmissions 606 and 314, andmobile station 308 receives beamformed transmissions 608 and 316.

Since base station 320 has eight transmit antenna beams (each antennabeams one stream of data streams), eight streams of beamformed data canbe formed at base station 320. Each mobile station can potentiallyreceive up to 2 streams (beams) of data in this example. If each of themobile stations 302, 304, 306, and 308 was limited to receive only asingle stream (beam) of data, instead of multiple streamssimultaneously, this would be multi-user beamforming (i.e., MU-BF).

A multi-user closed-loop transmit beamforming (MU-CLTB) scheme in MIMOsystems allows base station 320 to employ transmit beamforming and iscommunicated simultaneously to multiple mobile stations through the useof OFDM radio signals.

A practical closed-loop transmit beamforming scheme is typically basedon a codebook design. A codebook is a set of pre-determined antennabeams that are known to mobile stations. Closed-loop codebook-basedtransmit beamforming has been used for a scenario where a base stationforms a transmit antenna beam toward a single user at a time and at acertain frequency.

It has been known that a codebook based pre-coding MIMO can providesignificant spectral efficiency gain in the downlink closed-loop MIMO.In the IEEE 802.16e and 3GPP LTE standards, a 4 TX limited feedbackbased closed-loop MIMO configuration is supported. However, in IEEE802.16m and 3GPP LTE Advanced standards, in order to provide peakspectral efficiency, an 8 TX antenna configuration is proposed as aprominent precoding closed loop MIMO downlink system.

There is a tradeoff between the performance and the size of thecodebook. Having a large size codebook gives better performance thanhaving smaller number of codewords. However, the amount of performanceimprovement eventually decreases with an increase in codebook size. Inaddition, when rank adaptation is used, the large size of a codebookimplies a large amount of channel quality index (CQI) calculations.

As a practical scenario, a 10λ dimension is usually required for thewhole array at the BS (i.e., for a 8 Tx system, there is less than 1.5λof spacing between two adjacent antennas). This means the channel ishighly correlated at the BS side. In this correlated channel scenario, asmall codebook can provide sufficient spectral efficiency.

One of the strongest requirements of a codebook is to have a constantmodulus (CM) property as the baseline to ensure power amplifier balance.As a result of this constraint, designing codebook is similar todesigning equal gain transmission precoders.

Rank adaptation can be used to improve the spectral efficiency of lowgeometry users. When all of the lower rank codewords are reused forconstructing higher rank codewords, the codebook is said to have anested property. This nested property reduces the complexity required tocalculate the CQI when rank adaptation is performed.

From a system design point of view, it is beneficial if a largedimensional codeword is generated from a lower dimensional generatingvectors or matrices. This decreases the memory required to store thegenerating vectors or matrices and decreases the physical dimensions ofa system required to generate the codeword.

In the 3GPP LTE standard, a 4 TX codebook is generated based on theHouseholder reflection given the same dimensional 16 generating vectors.This requires a large memory size to store 64 elements of the generatingvectors. The main benefit of the Householder reflection is that it givesa 4×4 unitary matrix with a constant modulus property. However, the 4dimensional Householder reflection is the special case where theconstant modulus property is preserved. For the other dimensions, theconstant modulus property of the Householder reflection is broken. Sincethe constant modulus is the strongest requirement for the system,Householder reflection is not an appropriate approach for designing 8 TXcodebook including other dimensions.

The present disclosure provides a system and method for constructing aCM codebook that provides significant spectral efficiency gain in thedownlink of a closed-loop MIMO system without exception.

In one embodiment of the present disclosure, a systematic codebookdesign methodology for the constraint M-ary alphabet and for any2^(n)-dimensional antennas is provided.

In particular embodiments, a 4-bit codebook design for 8 TX antennaswith M-ary alphabet is provided. For the M-ary phase-shift keying(M-PSK) alphabet, a set of transformation matrices is defined as shownin Equation 2 below:

$\begin{matrix}{{{\Gamma_{M} = \left\{ {T_{1},T_{2},\ldots \mspace{14mu},T_{M/2}} \right\}},{where}}{T_{i} = \begin{bmatrix}1 & 1 \\^{{{j2\pi}{({i - 1})}}/M} & {- ^{{{j2\pi}{({i - 1})}}/M}}\end{bmatrix}}{for}{{i = 1},2,\ldots \mspace{14mu},{M/2.}}} & \left\lbrack {{Eqn}.\mspace{14mu} 2} \right\rbrack\end{matrix}$

The T_(i) forms a 2×2 unitary matrix and is used to transform thegeneration matrix used to construct the larger dimension matrix. Giventhe set of transformation matrix Γ_(M) for M-PSK, several complexHadamard (CH) transformations can be defined. For example, given any twogenerating matrix V₁ and V₂εU^(m×n), where U^(m×n) denotes the m×ndimensional matrix space whose columns are orthonormal each other, aone-stage complex Hadamard (CH) transformation can be defined as shownin Equation 3 belows:

$\begin{matrix}\begin{matrix}{{H_{i}\left( {V_{1},V_{2}} \right)} \equiv {\left( {T_{i} \otimes I_{m}} \right)\left\lbrack {{{I_{2}\left( {\text{:},1} \right)} \otimes V_{1}},{{I_{2}\left( {\text{:},2} \right)} \otimes V_{2}}} \right\rbrack}} \\{= \left\lbrack {{{T_{i}\left( {\text{:},1} \right)} \otimes V_{1}},{{T_{i}\left( {\text{:},2} \right)} \otimes V_{2}}} \right\rbrack} \\{{= W_{i}^{(1)}},}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 3} \right\rbrack\end{matrix}$

where I_(m) denotes the m-dimensional identity matrix, H_(i)(V₁,V₂)εU^(2m×2n),

denotes the Kronecker product, and superscript in the resulting matrixW_(i) ⁽¹⁾ denotes the number of the transformation stages.

FIG. 7 illustrates a one-stage CH transformation 700 according to anembodiment of this disclosure.

As shown in FIG. 7, when i==1, transformation 700 is equivalent to areal Hadamard transformation. With the one-stage complex Hadamardtransformation, a 2m×2n matrix with orthonormal columns is generated.

In a similar way, a two-stage complex Hadamard transformation can bedefined. Given any generating matrix V₁, V₂, V₃ and V₄εU^(m×n), a twostage complex Hadamard transformation is defined as shown in Equation 4below:

$\begin{matrix}\begin{matrix}{{H_{i,k,l}\left( {V_{1},V_{2},V_{3},V_{4}} \right)} \equiv {H_{i}\left( {W_{k}^{(1)},W_{l}^{(1)}} \right)}} \\{= {H_{i}\left( {{H_{k}\left( {V_{1},V_{2}} \right)},{H_{l}\left( {V_{3},V_{4}} \right)}} \right)}} \\{= \begin{bmatrix}{{{T_{i}\left( {\text{:},1} \right)} \otimes {H_{k}\left( {V_{1},V_{2}} \right)}},} \\{{T_{i}\left( {\text{:},1} \right)} \otimes {H_{l}\left( {V_{3},V_{4}} \right)}}\end{bmatrix}} \\{= \begin{pmatrix}{{{T_{i}\left( {\text{:},1} \right)} \otimes \begin{bmatrix}{{T_{k}\left( {\text{:},1} \right)} \otimes} \\{V_{1},{{T_{k}\left( {\text{:},2} \right)} \otimes V_{2}}}\end{bmatrix}},} \\{{T_{i}\left( {\text{:},1} \right)} \otimes \begin{bmatrix}{{T_{l}\left( {\text{:},1} \right)} \otimes} \\{V_{3},{{T_{l}\left( {\text{:},2} \right)} \otimes V_{4}}}\end{bmatrix}}\end{pmatrix}} \\{{= W_{i}^{(2)}},}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 4} \right\rbrack\end{matrix}$

where 1≦i,k,l≦M/2 and the resulting matrix W_(i) ⁽²⁾ forms a 4m×4nmatrix with orthonormal columns.

FIG. 8 illustrates a two-stage CH transformation 800 according to anembodiment of this disclosure.

This kind of extension can be performed to N-stage transformations toconstruct an Nm×Nn matrix by recursively applying the transformations.

FIG. 9 illustrates an N-stage CH transformation 900 according to anembodiment of this disclosure.

If the entries of the generating matrice V_(j) are restricted to the setof M-PSK alphabets, the above described N-stage CH transformation 900defined in M-PSK alphabet as shown in Equation 4 provides a convenientway of generating a set of Nm×Nn matrices with M-PSK entries. A simpleway to define a set of M-PSK generating matrix is to restrict V_(j) toΓ_(M), i.e. V_(j)εΓ_(M). Accordingly, the CH transformation 900 definedfor an M-PSK alphabet provides a convenient way of generating a set of2^(N)×2^(N) unitary matrices with M-PSK alphabets. The resulting unitarymatrix contains a rotation of the block diagonal matrix that provides agood channel matching property with dual-polarized antennas given theappropriate column subset selection for the different rank oftransmissions.

Using the above defined complex Hadamard transformations shown inEquation 4, a discrete Fourier transform (DFT) matrix is constructed byperforming a simple column permutation. For example, a 4-dimensional DFTmatrix can be constructed with the one-stage transformation shown inEquation 5 below:

$\begin{matrix}\begin{matrix}{{DFT}_{4} = {\frac{1}{\sqrt{4}}{H_{1}\left( {T_{1},T_{3}} \right)}P_{4}}} \\{{{- {\frac{1}{\sqrt{4}}\left\lbrack {{{T_{1}\left( {\text{:},1} \right)} \otimes T_{1}},{{T_{1}\left( {\text{:},2} \right)} \otimes T_{3}}} \right\rbrack}}P_{4}},}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 5} \right\rbrack\end{matrix}$

where P₄ denotes the column permutation matrix:

$P_{4} = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & 1\end{bmatrix}.}$

An 8-dimensional DFT matrix can also be constructed with the two-stagestransformations shown in Equation 6 below:

$\begin{matrix}\begin{matrix}{{DFT}_{8} = {\frac{1}{\sqrt{8}}{H_{1}\left( {{H_{3}\left( {T_{1},T_{3}} \right)},{H_{3}\left( {T_{2},T_{4}} \right)}} \right)}P_{8}}} \\{{= {\frac{1}{\sqrt{8}}\begin{pmatrix}{{{T_{1}\left( {\text{:},1} \right)} \otimes \begin{bmatrix}{{{T_{3}\left( {\text{:},1} \right)} \otimes T_{1}},} \\{{T_{3}\left( {\text{:},2} \right)} \otimes T_{2}}\end{bmatrix}},} \\{{T_{1}\left( {\text{:},1} \right)} \otimes \begin{bmatrix}{{{T_{3}\left( {\text{:},1} \right)} \otimes T_{2}},} \\{{T_{3}\left( {\text{:},2} \right)} \otimes T_{4}}\end{bmatrix}}\end{pmatrix}P_{8}}},}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 6} \right\rbrack\end{matrix}$

where P₈ denotes the column permutation matrix:

$P_{8} = {\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}.}$

Since the effect of the column permutation matrix can be merged with thecolumn subset strategy of the base matrix, the designed codebook caninclude the DFT matrix itself as a base matrix in some embodiments ofthe present disclosure.

In another embodiment of the present disclosure, a 4-bit 8 TX codebookwith an 8-PSK alphabet using the disclosed unitary matrix constructionsystem and method is provided. Given the nested property incorporatedwith rank adaptation, an 8 TX transmit precoder is constructed as acolumn subset of the unitary base matrix. For the 8 TX case, a two-stagecomplex Hadamard (CH) transformation is used to generate a set of 8×8base matrices. For notational convenience, the two-stage transformationis redefined as shown in Equation 7 below:

$\begin{matrix}\begin{matrix}{{H_{i,k,l}\left( {T_{m\; 1},T_{m\; 2},T_{m\; 3},T_{m\; 4}} \right)} \equiv {H_{i,k,l}\left( {{m\; 1},{m\; 2},{m\; 3},{m\; 4}} \right)}} \\{= \begin{pmatrix}{{{T_{i}\left( {\text{:},1} \right)} \otimes \left\lbrack {H_{k}\left( {{m\; 1},{m\; 2}} \right)} \right\rbrack},} \\{{T_{i}\left( {\text{:},2} \right)} \otimes \left\lbrack {H_{l}\left( {{m\; 3},{m\; 4}} \right)} \right\rbrack}\end{pmatrix}} \\{= {{H_{i}\left( {{H_{k}\left( {{m\; 1},{m\; 2}} \right)}{H_{l}\left( {{m\; 3},{m\; 4}} \right)}} \right)}.}}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 7} \right\rbrack\end{matrix}$

FIG. 10A illustrates a codebook that shows a mapping from a base matrixto a codeword according to an embodiment of this disclosure. Only thecolumn indices of the corresponding base matrices are shown in codebook1000 for brevity.

Codebook 1000 is non-QPSK based. The 4-bit 8 TX codebook 1000 isconstructed based on two 8×8 base matrices. Such a codebook is designedto work well with SP antenna configurations and is aimed to support bothSU-MIMO and MU-MIMO. That is, the codebook is designed to optimize bothan uncorrelated antenna array (SU-MIMO) and a correlated antenna array(MU-MIMO).

The base codebook is constructed from two matrices V8(:,:,1) andV8(:,:,2), which are constructed as described in Equation 8 below where:

${{T\; 1} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},{{T\; 2} = \begin{bmatrix}1 & 1 \\\frac{1 + j}{\sqrt{2}} & {- \frac{1 + j}{\sqrt{2}}}\end{bmatrix}},{{T\; 3} = \begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}},{and}$ ${T\; 4} = \begin{bmatrix}1 & 1 \\\frac{{- 1} + j}{\sqrt{2}} & {- \frac{{- 1} + j}{\sqrt{2}}}\end{bmatrix}$

are used to define

$\begin{matrix}\begin{matrix}{{H_{i}\left( {{m\; 1},{m\; 2}} \right)} \equiv {H_{i}\left( {T_{{m\; 1},}T_{m\; 2}} \right)}} \\{{= \left\lbrack {{{T_{i}\left( {\text{:},1} \right)} \otimes T_{m\; 1}},{{T_{i}\left( {\text{:},2} \right)} \otimes T_{m\; 2}}} \right\rbrack},{and}}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 8} \right\rbrack \\\begin{matrix}{{H_{i,k,l}\left( {T_{m\; 1},T_{m\; 2},T_{m\; 3},T_{m\; 4}} \right)} \equiv {H_{i,k,l}\left( {{m\; 1},{m\; 2},{m\; 3},{m\; 4}} \right)}} \\{= \begin{pmatrix}{{{T_{i}\left( {\text{:},1} \right)} \otimes \left\lbrack {H_{k}\left( {{m\; 1},{m\; 2}} \right)} \right\rbrack},} \\{{T_{i}\left( {\text{:},2} \right)} \otimes \left\lbrack {H_{l}\left( {{m\; 3},{m\; 4}} \right)} \right\rbrack}\end{pmatrix}} \\{= {{H_{i}\left( {{H_{k}\left( {{m\; 1},{m\; 2}} \right)}{H_{l}\left( {{m\; 3},{m\; 4}} \right)}} \right)}.}}\end{matrix} & \;\end{matrix}$

With regard to codebook 1000, the numbers shown in the column for eachrank refer to the column index of the matrices V8(:,:,1) and V8(:,:,2).

FIG. 10B illustrates a table 1010 further describing rank 1 of thecodebook 1000 of FIG. 10A according to an embodiment of this disclosure.

FIG. 11 illustrates two rank-8 matrices 1110 and 1120 according to anembodiment of this disclosure.

In a particular embodiment, the rank-1 8 TX beamforming codebook isoptimized for correlated antenna arrays. The base matrix of thedisclosed rank-1 8 TX codebook is denoted as V8(:,:,3), and the size ofthe base matrix V8(:,:,3) is 8×16. The j-th column vector of the basematrix V8(:,:,3) is given by Equation 9 below:

$\begin{matrix}{{{V_{8}\left( {\text{:},k,3} \right)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}1 \\^{{{j\pi}\sin}{(\theta_{k})}} \\^{{{j2\pi}\sin}{(\theta_{k})}} \\^{{{j3\pi}\sin}{(\theta_{k})}} \\^{{{j4\pi}\sin}{(\theta_{k})}} \\^{{{j5\pi}\sin}{(\theta_{k})}} \\^{{{j6\pi}\sin}{(\theta_{k})}} \\^{{{j7\pi}\sin}{(\theta_{k})}}\end{bmatrix}}},} & \left\lbrack {{Eqn}.\mspace{14mu} 9} \right\rbrack\end{matrix}$

where k=1, 2, . . . 16.

One example of the set of θ_(j), k=1, . . . , 16, is a set where allbeams have uniform angular spacing. In particular, in a 3-sector systemwhere each sector has 120 degrees angular spacing, the set θ_(j), k=1, .. . , 16, is given by Equation 10 below:

$\begin{matrix}{\theta_{k} = {{\left( {\left( {k - 1} \right) + {1/2}} \right)*\frac{\pi}{24}} - {\frac{\pi}{3}\mspace{14mu} ({degrees})}}} & \left\lbrack {{Eqn}.\mspace{14mu} 10} \right\rbrack\end{matrix}$

if the reference angle (i.e, the 0-degree direction) corresponds to thephase center of the antenna array.

FIG. 12 illustrates a codebook 1200 that shows a mapping from a basematrix to a codeword according to another embodiment of this disclosure.Only the column indices of the corresponding base matrices are shown incodebook 1200 for brevity.

Codebook 1200 is non-QPSK based and is constructed from four 8×8 basematrices. Codebook 1200 is designed to work well with an SP antennaconfiguration and is aimed to support both SU-MIMO and MU-MIMO. That is,codebook 1200 is designed to optimize both an uncorrelated antenna array(SU-MIMO) and a correlated antenna array (MU-MIMO).

In some embodiments, codebook 1200 is a 3-bit 8 TX codebook. In aparticular embodiment, the base matrix V8(:,:,4) is used for rank-1transmission while the base matrix V8(:,:,2) is used for transmissionswith a rank greater than or equal to 2.

In a further particular embodiment, the disclosed rank-1 8 TXbeamforming codebook is optimized for a correlated antenna array in a3-sector system where each sector has 120 degrees angular spacing. Thebase matrix of the disclosed rank-1 8TX codebook is denoted asV8(:,:,4), and the size of the base matrix V8(:,:,4) is 8×8. The j-thcolumn vector of the base matrix V8(:,:,4) is given by Equation 11below:

$\begin{matrix}{{V_{8}\left( {\text{:},k,4} \right)} = {{\frac{1}{\sqrt{8}}\begin{bmatrix}1 \\^{{{j\pi}\sin}{(\theta_{k})}} \\^{{{j2\pi}\sin}{(\theta_{k})}} \\^{{{j3\pi}\sin}{(\theta_{k})}} \\^{{{j4\pi}\sin}{(\theta_{k})}} \\^{{{j5\pi}\sin}{(\theta_{k})}} \\^{{{j6\pi}\sin}{(\theta_{k})}} \\^{{{j7\pi}\sin}{(\theta_{k})}}\end{bmatrix}}.}} & \left\lbrack {{Eqn}.\mspace{14mu} 11} \right\rbrack\end{matrix}$

where k=1, 2, . . . 8.

In yet another particular embodiment, θ_(j), k=1, . . . , 8, is a setwhere all beams have uniform angular spacing as shown in Equation 12below:

$\begin{matrix}{\theta_{k} = {{\left( {\left( {k - 1} \right) + {1/2}} \right)*\frac{\pi}{12}} - {\frac{\pi}{3}({degrees})}}} & \left\lbrack {{Eqn}.\mspace{14mu} 12} \right\rbrack\end{matrix}$

if the reference angle (i.e, the 0-degree direction) corresponds to thephase center of the antenna array.

With regard to codebook 1200, the numbers shown in the column for eachrank refer to the column index of the matrices V8(:,:,2) and V8(:,:,4).

FIG. 13 illustrates a codebook 1300 that shows a mapping from a basematrix to a codeword according to a further embodiment of thisdisclosure. Only the column indices of the corresponding base matricesare shown in codebook 1300 for brevity.

Codebook 1300 is non-QPSK based and is constructed from eight 8×8 basematrices. Codebook 1300 is designed to work well with SP antennaconfigurations and is aimed to support both SU-MIMO and MU-MIMO. Thatis, codebook 1300 is designed to optimize both an uncorrelated antennaarray (SU-MIMO) and a correlated antenna array (MU-MIMO).

In some embodiments, codebook 1300 is a 3-bit 8 TX codebook. In aparticular embodiment, the base matrix V8(:,:,4) is used for rank-1transmission while the base matrix V8(:,:,1) is used for transmissionswith a rank greater than or equal to 2.

With regard to codebook 1300, the numbers shown in the column for eachrank refer to the column index of the matrices V8(:,:,1) and V8(:,:,4).

FIG. 14 illustrates a codebook 1400 that shows a mapping from a basematrix to a codeword according to yet another embodiment of thisdisclosure. Only the column indices of the corresponding base matricesare shown in codebook 1400 for brevity.

Codebook 1400 is non-QPSK based. Codebook 1400 is designed to work wellwith SP antenna configuration and is aimed to support both SU-MIMO andMU-MIMO. That is, the codebook is designed to optimize both anuncorrelated antenna array (SU-MIMO) and a correlated antenna array(MU-MIMO).

In some embodiments, codebook 1400 is a 3-bit 8 TX codebook. In aparticular embodiment, the base matrix V8(:,:,5) is used for rank-1transmission while the base matrix V8(:,:,2) or V8(:,:,1) is used fortransmissions with a rank greater than or equal to 2.

In one embodiment, the disclosed rank-1 8 TX beamforming codebook 1400is optimized for a correlated antenna array in a 3-sector system whereeach sector has 120 degrees angular spacing. One example of the set ofθ_(j), j=1, . . . , 8, is a set where all beams have uniform angularspacing is given by Equation 13 below:

$\begin{matrix}{{{V_{8}\left( {\text{:},k,5} \right)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}1 \\^{{j2\pi}*D*{\sin {(\theta_{k})}}} \\^{{j2\pi}*2*D*{\sin {(\theta_{k})}}} \\^{{j2\pi}*3*D*{\sin {(\theta_{k})}}} \\^{{j2\pi}*4*D*{\sin {(\theta_{k})}}} \\^{{j2\pi}*5*D*{\sin {(\theta_{k})}}} \\^{{j2\pi}*6*D*{\sin {(\theta_{k})}}} \\^{{j2\pi}*7*D*{\sin {(\theta_{k})}}}\end{bmatrix}}},} & \left\lbrack {{Eqn}.\mspace{14mu} 13} \right\rbrack\end{matrix}$

where k=1, 2, . . . 8.

where D is the minimum antenna spacing between two antenna elements in alinear antenna array and is expressed as a number of wavelengths. Oneexample of the set of θ_(j), k=1, . . . , 8, is a set where all beamshave uniform angular spacing is given by Equation 14 below:

$\begin{matrix}{\theta_{k} = {{\left( {\left( {k - 1} \right) + {1/2}} \right)*\frac{\pi}{12}} - {\frac{\pi}{3}({degrees})}}} & \left\lbrack {{Eqn}.\mspace{14mu} 14} \right\rbrack\end{matrix}$

if the reference angle (i.e, the 0-degree direction) corresponds to thephase center of the antenna array.

With regard to codebook 1400, the numbers shown in the column for eachrank refer to the column index of the matrices V8(:,:,1), V8(:,:,2) andV8(:,:,5).

In particular embodiments, codebooks 1200, 1300, and 1400 are 3-bitcodebook and are designed to work well with SP antenna configurations.These three codebooks are aimed to support both SU-MIMO and MU-MIMOoperations. That is, codebooks 1200, 1300, and 1400 are designed tooptimize both an uncorrelated antenna array (SU-MIMO) and a correlatedantenna array (MU-MIMO).

In another embodiment, a codebook subset restriction rule is used forthese three codebooks. In a particular embodiment, the CW (code word)size of these codebooks is 16. This means that it normally requires 4bits to carry 16 CWs. In such an embodiment, a subset of these threecodebooks is used. In a particular embodiment, 3 bits are used to carry8 CWs. Using such a codebook subset restriction allows SU-MIMO andMU-MIMO operations to be jointly optimized. That is, for rank-1transmission, the base matrix W4 or W5 is used to optimize a correlatedarray for MU-MIMO operation while the base matrix W2 or W1 is used forthe case where the rank of transmission is greater than or equal to 2,which is optimized for an uncorrelated antenna array for SU-MIMOoperation.

The number of column vectors of V8(:,:,1), V8(:,:,2), V8(:,:,4), andV8(:,:,5) base matrix is 8, which requires only 3 bits to represent the8 column vectors. Because the disclosed codebooks and subset restrictionis used for closed-loop SU-MIMO and MU operations, a mobile station oruser terminal (UE) reports CQI (channel quality index) to its servingbase stations. The reported CQI includes the rank of the codebook andthe CW index for a reported rank (namely, PMI (precoder matrix index) orPVI (precoder vector index)).

FIG. 15 illustrates a codebook 1500 that shows a mapping from a basematrix to a codeword according to yet another embodiment of thisdisclosure. Only the column indices of the corresponding base matricesare shown in codebook 1500 for brevity.

Codebook 1500 is designed to work well with an SP antenna configurationand is aimed to have a minimum number of base matrices (i.e., two basematrices). The entries of the two base matrices are given by Equations15 and 16 below:

$\begin{matrix}\begin{matrix}{W_{1} = {\frac{1}{\sqrt{8}}{H_{1,1,1}\left( {1,1,1,1} \right)}}} \\{{= {\frac{1}{\sqrt{8}}\begin{bmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\1 & {- 1} & 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} & 1 \\1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} & {- 1} & 1 & {- 1} & 1 \\1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 \\1 & {- 1} & {- 1} & 1 & {- 1} & 1 & 1 & {- 1}\end{bmatrix}}},{and}}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 15} \right\rbrack \\\begin{matrix}{W_{2} = {\frac{1}{\sqrt{8}}{H_{3,3,3}\left( {3,3,3,3} \right)}}} \\{= {{\frac{1}{\sqrt{8}}\begin{bmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\j & {- j} & j & {- j} & j & {- j} & j & {- j} \\j & j & {- j} & {- j} & j & j & {- j} & {- j} \\{- 1} & 1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} \\j & j & j & j & {- j} & {- j} & {- j} & {- j} \\{- 1} & 1 & {- 1} & 1 & 1 & {- 1} & 1 & {- 1} \\{- 1} & {- 1} & 1 & 1 & 1 & 1 & {- 1} & {- 1} \\{- j} & j & j & {- j} & j & {- j} & {- j} & j\end{bmatrix}}.}}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 16} \right\rbrack\end{matrix}$

As shown in FIG. 15, codebook 1500 consists of a QPSK alphabet only, andthe codewords are extracted from two 8×8 unitary base matrices. The basematrices are designed using the two-stage complex Hadamardtransformations. In terms of CQI calculation, the disclosed codebook1500 computes HF_(i) for i=1, . . . , 16 for the rank-1 precoder F_(i),where H denotes the channel matrix, and for the other ranks, previouslycomputed values are reused.

With regard to codebook 1500, the numbers shown in the column for eachrank refer to the column index of the matrices

$W_{2} = {{\frac{1}{\sqrt{8}}{H_{3,3,3}\left( {3,3,3,3} \right)}{\mspace{11mu} \;}{and}\mspace{14mu} W_{2}} = {\frac{1}{\sqrt{8}}{{H_{3,3,3}\left( {3,3,3,3} \right)}.}}}$

FIG. 16 is a diagram 1600 illustrating a system's performance utilizingcodebook 1000 when MU-MIMO is employed at a base station according to anembodiment of this disclosure.

FIG. 16 shows the system throughput of a base station when itcommunicates with multiple mobile stations throughput the use of MU-MIMOschemes. The system throughput is the average throughput per basestation. In this figure, it is assumed that an 8 transmit antenna arrayis employed at a base station and a 2 receive antenna array is employedat a user terminal. A line 1610 is used to indicate the systemthroughput using codebook 1000. A line 1620 is used to indicate thesystem throughput of the prior art method. The results show that themethod provided in the present disclosure provides a significant gainover the prior art method.

FIG. 17 illustrates a method 1700 of operating a base station accordingto an embodiment of this disclosure.

As shown in FIG. 17, a base station selects a codeword from any of thecodebooks disclosed in the present disclosure (block 1710). For example,the base station may select a codeword from codebook 1000, 1200, 1300,1400, or 1500. The base station precodes data with the selected codeword(block 1720) and transmits the data using the selected codeword (block1730). The base station then receives CQI information related to thetransmitted data (block 1740) and determines if the selected codeword isto be used for further data transmission based at least partly upon thereceived CQI information (block 1750). If the base station decides touse the selected codeword, the base station continues communicatingusing the selected codeword (block 1760). If the base station decidesnot to use the selected codeword, the base station selects anothercodeword from the codebook (block 1710).

In one embodiment, the base station may determine if the selectedcodeword is to be used for further data transmission by comparing thereceived CQI information with a pre-determined value. If the receivedCQI information is equal to or greater than the pre-determined value,the base station uses the selected codeword for further datatransmission. If the received CQI information is less than thepre-determined value, the base station does not use the selectedcodeword for further data transmission and selects another codeword fromthe codebook. In another embodiment, the base station may transmit datausing all of the codewords in the codebook and selects the codewordassociated with the best CQI information.

FIG. 18 illustrates a method 1800 of operating a mobile or subscriberstation according to an embodiment of this disclosure.

As shown in FIG. 18, a subscriber station receives data precoded using acodeword selected from a codebook disclosed in the present disclosure(block 1810). For example, the codeword may be selected from codebook1000, 1200, 1300, 1400, or 1500. The subscriber station transmits CQIinformation related to the precoded data (1820). The subscriber stationthen maintains communication using the selected codeword (1830).

Although the codebooks of this disclosure are described in terms ofbeing 3-bit or 4-bit codebooks, one of ordinary skill in the art wouldrecognize that the codebooks provided in this disclosure may beimplemented in codebooks having a larger size without departing from thescope or spirit of this disclosure. Similarly, although the codebooks ofthis disclosure are described in terms of being used with 8 TX antennabeamforming, one of ordinary skill in the art would recognize that thecodebooks provided in this disclosure may be expanded to accommodatebeamforming schemes utilizing more than 8 TX antennas without departingfrom the scope or spirit of this disclosure.

Although the present disclosure has been described with an exemplaryembodiment, various changes and modifications may be suggested to oneskilled in the art. It is intended that the present disclosure encompasssuch changes and modifications as fall within the scope of the appendedclaims.

1.-33. (canceled)
 34. A base station including a multiple antenna arrayfor wireless communication, comprising: a codebook; a processor toselect a codeword from the codebook and to code data with the selectedcodeword; and a transmitter to transmit the coded data, whereincodewords in the codebook are based on values shown in the followingtable: V8(:, CMI, 3) = [c1, c2, . . . c8]; CMI c1 c2 c3 c4 c5 c6 c7 c8 10.3536 −0.3051 −   0.1732 + 0.0062 − −0.1839 + 0.3112 − −0.3533 −0.2987 + 0.1786i 0.3082i 0.3535i 0.3020i 0.1677i 0.0124i 0.1892i 20.3536 −0.2514 −   0.0041 + 0.2456 − −0.3535 + 0.2571 + −0.0123 −−0.2397 +   0.2486i 0.3535i 0.2543i 0.0082i 0.2427i 0.3533i 0.2599i 30.3536 −0.1697 − −0.1907 + 0.3527 + −0.1479 − −0.2107 +     0.3502 +−0.1254 −   0.3102i 0.2977i 0.0244i 0.3211i 0.2839i 0.0486i 0.3306i 40.3536 −0.0614 − −0.3322 + 0.1768 +   0.2708 − −0.2709 −   −0.1767 +0.3323 + 0.3482i 0.1210i 0.3062i 0.2273i 0.2272i 0.3062i 0.1208i 50.3536   0.0638 − −0.3306 − −0.1830 +     0.2646 + 0.2784 − −0.1642 −−0.3376 +   0.3478i 0.1254i 0.3025i 0.2345i 0.2180i 0.3131i 0.1050i 60.3536   0.1881 − −0.1534 − −0.3513 −   −0.2204 + 0.1168 +   0.3447 +0.2499 − 0.2994i 0.3185i 0.0395i 0.2764i 0.3337i 0.0786i 0.2501i 70.3536   0.2892 −   0.1196 − −0.0936 −   −0.2727 − −0.3525 −   −0.3040 +−0.1449 +   0.2034i 0.3327i 0.3409i 0.2251i 0.0272i 0.1805i 0.3225i 80.3536   0.3461 −   0.3241 − 0.2885 −   0.2407 − 0.1828 −   0.1172 −0.0467 − 0.0721i 0.1412i 0.2044i 0.2590i 0.3026i 0.3336i 0.3505i 90.3536   0.3461 +   0.3241 + 0.2885 +   0.2407 + 0.1828 +   0.1172 +0.0467 − 0.0721i 0.1412i 0.2044i 0.2590i 0.3026i 0.3336i 0.3505i 100.3536   0.2892 +   0.1196 + −0.0936 +   −0.2727 + −0.3525 +   −0.3040 −−0.1449 −   0.2034i 0.3327i 0.3409i 0.2251i 0.0272i 0.1805i 0.3225i 110.3536   0.1881 + −0.1534 + −0.513 +   −0.2204 − 0.1168 −   0.3447 −0.2499 + 0.2994i 0.3185i 0.0395i 0.2764i 0.3337i 0.0786i 0.2501i 120.3536   0.0638 + −0.3306 + −0.1830 −     0.2646 − 0.2784 + −0.1642 +−0.3376 −   0.3478i 0.1254i 0.3025i 0.2345i 0.2180i 0.3131i 0.1050i 130.3536 −0.0614 + −0.3322 − 0.1768 −   0.2708 + −0.2709 +   −0.1767 −0.3323 − 0.3482i 0.1210i 0.3062i 0.2273i 0.2272i 0.3062i 0.1208i 140.3536 −0.1697 + −0.1907 − 0.3527 − −0.1479 + −0.2107 −     0.3502 −−0.1254 +   0.3102i 0.2977i 0.0244i 0.3211i 0.2839i 0.0486i 0.3306i 150.3536 −0.2514 +   0.0041 − 0.2456 + −0.3535 − 0.2571 − −0.0123 +−0.2397 −   0.2486i 0.3535i 0.2543i 0.0082i 0.2427i 0.3533i 0.2599i 160.3536 −0.3051 +   0.1732 − 0.0062 + −0.1839 − 0.3112 + −0.3533 + 0.2987− 0.1786i 0.3082i 0.3535i 0.3020i 0.1677i 0.0124i 0.1892i

where each row represents a Codebook Matrix Index (CMI) and each column(c1˜c8) represents an antenna in the multiple antenna array.
 35. Thebase station of claim 34, wherein the values in the table are obtainedbased on the following equation:${{V_{8}\left( {\text{:},k,3} \right)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}1 \\^{{{j\pi}\sin}{(\theta_{k})}} \\^{{{j2\pi}\sin}{(\theta_{k})}} \\^{{{j3\pi}\sin}{(\theta_{k})}} \\^{{{j4\pi}\sin}{(\theta_{k})}} \\^{{{j5\pi}\sin}{(\theta_{k})}} \\^{{{j6\pi}\sin}{(\theta_{k})}} \\^{{{j7\pi}\sin}{(\theta_{k})}}\end{bmatrix}}},$ where k=1, 2, 3, . . . , 16, and k represents the CMI.36. The base station of claim 35, wherein θ_(k) is given by thefollowing equation:${\theta_{k} = {{\left( {\left( {k - 1} \right) + {1/2}} \right)*\frac{\pi}{24}} - \frac{\pi}{3}}},$where k=1, 2, 3, . . . , 16, and k represents the CMI.
 37. The basestation of claim 34, wherein the codebook is a 4-bit codebook.
 38. Thebase station of claim 34, wherein the table includes real and imaginaryvalues for the second to eighth antennas (c2˜c8) of the multiple antennaarray for each CMI.
 39. A base station including a multiple antennaarray for wireless communication, comprising: a codebook; a processor toselect a codeword from the codebook and to code data with the selectedcodeword; and a transmitter to transmit the coded data, whereincodewords in the codebook are based on the following equation:${{V_{8}\left( {\text{:},k,3} \right)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}1 \\^{{{j\pi}\sin}{(\theta_{k})}} \\^{{{j2\pi}\sin}{(\theta_{k})}} \\^{{{j3\pi}\sin}{(\theta_{k})}} \\^{{{j4\pi}\sin}{(\theta_{k})}} \\^{{{j5\pi}\sin}{(\theta_{k})}} \\^{{{j6\pi}\sin}{(\theta_{k})}} \\^{{{j7\pi}\sin}{(\theta_{k})}}\end{bmatrix}}},$ where k=1, 2, 3, . . . ,
 16. 40. The base station ofclaim 39, wherein θ_(k) is given by the following equation:${\theta_{k} = {{\left( {\left( {k - 1} \right) + {1/2}} \right)*\frac{\pi}{24}} - \frac{\pi}{3}}},$where k=1, 2, 3, . . . ,
 16. 41. The base station of claim 39, whereinthe codebook is a 4-bit codebook.
 42. The base station of claim 39,wherein the codewords in the codebook account for real and imaginarycomponents of one or more antennas of the multiple antenna array.
 43. Amethod for coding data in a base station including a multiple antennaarray for wireless communication, the method comprising: selecting acodeword from a codebook; coding data with the selected codeword; andtransmitting the coded data, wherein codewords in the codebook are basedon values shown in the following table: V8(:, CMI, 3) = [c1, c2, . . .c8]; CMI c1 c2 c3 c4 c5 c6 c7 c8 1 0.3536 −0.3051 −     0.1732 + 0.0062− −0.1839 + 0.3112 − −0.3533 −   0.2987 + 0.1786i 0.3082i 0.3535i0.3020i 0.1677i 0.0124i 0.1892i 2 0.3536 −0.2514 −     0.0041 + 0.2456 −−0.3535 + 0.2571 + −0.0123 − −0.2397 + 0.2486i 0.3535i 0.2543i 0.0082i0.2427i 0.3533i 0.2599i 3 0.3536 −0.1697 −   −0.1907 + 0.3527 + −0.1479− −0.2107 +     0.3502 + −0.1254 − 0.3102i 0.2977i 0.0244i 0.3211i0.2839i 0.0486i 0.3306i 4 0.3536 −0.0614 −   −0.3322 + 0.1768 +   0.2708− −0.2709 −   −0.1767 +   0.3323 + 0.3482i 0.1210i 0.3062i 0.2273i0.2272i 0.3062i 0.1208i 5 0.3536 0.0638 − −0.3306 − −0.1830 +    0.2646 + 0.2784 − −0.1642 − −0.3376 + 0.3478i 0.1254i 0.3025i 0.2345i0.2180i 0.3131i 0.1050i 6 0.3536 0.1881 − −0.1534 − −0.3513 −  −0.2204 + 0.1168 +   0.3447 +   0.2499 − 0.2994i 0.3185i 0.0395i 0.2764i0.3337i 0.0786i 0.2501i 7 0.3536 0.2892 −   0.1196 − −0.0936 −   −0.2727− −0.3525 −   −0.3040 + −0.1449 + 0.2034i 0.3327i 0.3409i 0.2251i0.0272i 0.1805i 0.3225i 8 0.3536 0.3461 −   0.3241 − 0.2885 −   0.2407 −0.1828 −   0.1172 −   0.0467 − 0.0721i 0.1412i 0.2044i 0.2590i 0.3026i0.3336i 0.3505i 9 0.3536 0.3461 +   0.3241 + 0.2885 +   0.2407 +0.1828 +   0.1172 +   0.0467 − 0.0721i 0.1412i 0.2044i 0.2590i 0.3026i0.3336i 0.3505i 10 0.3536 0.2892 +   0.1196 + −0.0936 +   −0.2727 +−0.3525 +   −0.3040 − −0.1449 − 0.2034i 0.3327i 0.3409i 0.2251i 0.0272i0.1805i 0.3225i 11 0.3536 0.1881 + −0.1534 + −0.3513 +   −0.2204 −0.1168 −   0.3447 −   0.2499 + 0.2994i 0.3185i 0.0395i 0.2764i 0.3337i0.0786i 0.2501i 12 0.3536 0.0638 + −0.3306 + −0.1830 −     0.2646 −0.2784 + −0.1642 + −0.3376 − 0.3478i 0.1254i 0.3025i 0.2345i 0.2180i0.3131i 0.1050i 13 0.3536 −0.0614 +   −0.3322 − 0.1768 −   0.2708 +−0.2709 +   −0.1767 −   0.3323 − 0.3482i 0.1210i 0.3062i 0.2273i 0.2272i0.3062i 0.1208i 14 0.3536 −0.1697 +   −0.1907 − 0.3527 − −0.1479 +−0.2107 −     0.3502 − −0.1254 + 0.3102i 0.2977i 0.0244i 0.3211i 0.2839i0.0486i 0.3306i 15 0.3536 −0.2514 +     0.0041 − 0.2456 + −0.3535 −0.2571 − −0.0123 + −0.2397 − 0.2486i 0.3535i 0.2543i 0.0082i 0.2427i0.3533i 0.2599i 16 0.3536 −0.3051 +     0.1732 − 0.0062 + −0.1839 −0.3112 + −0.3533 +   0.2987 − 0.1786i 0.3082i 0.3535i 0.3020i 0.1677i0.0124i 0.1892i

where each row represents a Codebook Matrix Index (CMI) and each column(c1˜c8) represents an antenna in the multiple antenna array.
 44. Themethod of claim 43, wherein the values in the table are obtained basedon the following equation:${{V_{8}\left( {\text{:},k,3} \right)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}1 \\^{{{j\pi}\sin}{(\theta_{k})}} \\^{{{j2\pi}\sin}{(\theta_{k})}} \\^{{{j3\pi}\sin}{(\theta_{k})}} \\^{{{j4\pi}\sin}{(\theta_{k})}} \\^{{{j5\pi}\sin}{(\theta_{k})}} \\^{{{j6\pi}\sin}{(\theta_{k})}} \\^{{{j7\pi}\sin}{(\theta_{k})}}\end{bmatrix}}},$ where k=1, 2, 3, . . . , 16, and k represents the CMI.45. The method of claim 44, wherein θ_(k) is given by the followingequation:${\theta_{k} = {{\left( {\left( {k - 1} \right) + {1/2}} \right)*\frac{\pi}{24}} - \frac{\pi}{3}}},$where k=1, 2, 3, . . . , 16, and k represents the CMI.
 46. The method ofclaim 45, wherein the codebook is a 4-bit codebook.
 47. The method ofclaim 46, wherein the table includes real and imaginary values for thesecond to eighth antennas (c2˜c8) of the multiple antenna array for eachCMI.
 48. A method for coding data in a base station including a multipleantenna array for wireless communication, comprising: selecting acodeword from a codebook; coding data with the selected codeword; andtransmitting the coded data, wherein codewords in the codebook are basedon the following equation:${{V_{8}\left( {\text{:},k,3} \right)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}1 \\^{{{j\pi}\sin}{(\theta_{k})}} \\^{{{j2\pi}\sin}{(\theta_{k})}} \\^{{{j3\pi}\sin}{(\theta_{k})}} \\^{{{j4\pi}\sin}{(\theta_{k})}} \\^{{{j5\pi}\sin}{(\theta_{k})}} \\^{{{j6\pi}\sin}{(\theta_{k})}} \\^{{{j7\pi}\sin}{(\theta_{k})}}\end{bmatrix}}},$ where k=1, 2, 3, . . . ,
 16. 49. The method of claim48, wherein θ_(k) is given by the following equation:${\theta_{k} = {{\left( {\left( {k - 1} \right) + {1/2}} \right)*\frac{\pi}{24}} - \frac{\pi}{3}}},$where k=1, 2, 3, . . . ,
 16. 50. The method of claim 48, wherein thecodebook is a 4-bit codebook.
 51. The method of claim 48, wherein thecodewords in the codebook account for real and imaginary components ofone or more antennas of the multiple antenna array.
 52. A data structurestored on a computer readable medium for coding data in a base stationincluding a multiple antenna array for wireless communication,comprising: a codebook from which to select a codeword for coding datawith the selected codeword, wherein codewords in the codebook are basedon values shown in the following table: V8(:, CMI, 3) = [c1, c2, . . .c8]; CMI c1 c2 c3 c4 c5 c6 c7 c8 1 0.3536 −0.3051 −   0.1732 + 0.0062 −−0.1839 + 0.3112 − −0.3533 −   0.2987 + 0.1786i 0.3082i 0.3535i 0.3020i0.1677i 0.0124i 0.1892i 2 0.3536 −0.2514 −   0.0041 + 0.2456 − −0.3535 +0.2571 + −0.0123 − −0.2397 + 0.2486i 0.3535i 0.2543i 0.0082i 0.2427i0.3533i 0.2599i 3 0.3536 −0.1697 − −0.1907 + 0.3527 + −0.1479 − −0.2107+     0.3502 + −0.1254 − 0.3102i 0.2977i 0.0244i 0.3211i 0.2839i 0.0486i0.3306i 4 0.3536 −0.0614 − −0.3322 + 0.1768 +   0.2708 − −0.2709 −  −0.1767 +   0.3323 + 0.3482i 0.1210i 0.3062i 0.2273i 0.2272i 0.3062i0.1208i 5 0.3536   0.0638 − −0.3306 − −0.1830 +     0.2646 + 0.2784 −−0.1642 − −0.3376 + 0.3478i 0.1254i 0.3025i 0.2345i 0.2180i 0.3131i0.1050i 6 0.3536   0.1881 − −0.1534 − −0.3513 −   −0.2204 + 0.1168 +  0.3447 +   0.2499 − 0.2994i 0.3185i 0.0395i 0.2764i 0.3337i 0.0786i0.2501i 7 0.3536   0.2892 −   0.1196 − −0.0936 −   −0.2727 − −0.3525 −  −0.3040 + −0.1449 + 0.2034i 0.3327i 0.3409i 0.2251i 0.0272i 0.1805i0.3225i 8 0.3536   0.3461 −   0.3241 − 0.2885 −   0.2407 − 0.1828 −  0.1172 −   0.0467 − 0.0721i 0.1412i 0.2044i 0.2590i 0.3026i 0.3336i0.3505i 9 0.3536   0.3461 +   0.3241 + 0.2885 +   0.2407 + 0.1828 +  0.1172 +   0.0467 − 0.0721i 0.1412i 0.2044i 0.2590i 0.3026i 0.3336i0.3505i 10 0.3536   0.2892 +   0.1196 + −0.0936 +   −0.2727 + −0.3525+   −0.3040 − −0.1449 − 0.2034i 0.3327i 0.3409i 0.2251i 0.0272i 0.1805i0.3225i 11 0.3536   0.1881 + −0.1534 + −0.3513 +   −0.2204 − 0.1168 −  0.3447 −   0.2499 + 0.2994i 0.3185i 0.0395i 0.2764i 0.3337i 0.0786i0.2501i 12 0.3536   0.0638 + −0.3306 + −0.1830 −     0.2646 − 0.2784 +−0.1642 + −0.3376 − 0.3478i 0.1254i 0.3025i 0.2345i 0.2180i 0.3131i0.1050i 13 0.3536 −0.0614 + −0.3322 − 0.1768 −   0.2708 + −0.2709 +  −0.1767 −   0.3323 − 0.3482i 0.1210i 0.3062i 0.2273i 0.2272i 0.3062i0.1208i 14 0.3536 −0.1697 + −0.1907 − 0.3527 − −0.1479 + −0.2107 −    0.3502 − −0.1254 + 0.3102i 0.2977i 0.0244i 0.3211i 0.2839i 0.0486i0.3306i 15 0.3536 −0.2514 +   0.0041 − 0.2456 + −0.3535 − 0.2571 −−0.0123 + −0.2397 − 0.2486i 0.3535i 0.2543i 0.0082i 0.2427i 0.3533i0.2599i 16 0.3536 −0.3051 +   0.1732 − 0.0062 + −0.1839 − 0.3112 +−0.3533 +   0.2987 − 0.1786i 0.3082i 0.3535i 0.3020i 0.1677i 0.0124i0.1892i

where each row represents a Codebook Matrix Index (CMI) and each column(c1˜c8) represents an antenna in the multiple antenna array.
 53. Thedata structure of claim 52, wherein the values in the table are obtainedbased on the following equation:${{V_{8}\left( {\text{:},k,3} \right)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}1 \\^{{{j\pi}\sin}{(\theta_{k})}} \\^{{{j2\pi}\sin}{(\theta_{k})}} \\^{{{j3\pi}\sin}{(\theta_{k})}} \\^{{{j4\pi}\sin}{(\theta_{k})}} \\^{{{j5\pi}\sin}{(\theta_{k})}} \\^{{{j6\pi}\sin}{(\theta_{k})}} \\^{{{j7\pi}\sin}{(\theta_{k})}}\end{bmatrix}}},$ where k=1, 2, 3, . . . , 16, and k represents the CMI.54. The data structure of claim 53, wherein θ_(k) is given by thefollowing equation:${\theta_{k} = {{\left( {\left( {k - 1} \right) + {1/2}} \right)*\frac{\pi}{24}} - \frac{\pi}{3}}},$where k=1, 2, 3, . . . , 16, and k represents the CMI.
 55. The datastructure of claim 52, wherein the codebook is a 4-bit codebook.
 56. Thedata structure of claim 52, wherein the table includes real andimaginary values for the second to eighth antennas (c2˜c8) of themultiple antenna array for each CMI.